Problem: This is the easy version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.

Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version all prices are different.

An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.

You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.

Input

The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.

The second line contains n different integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.

Output

In the first line print the maximum number of ice spheres that Sage can buy.

In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.

Example

Input


5
1 2 3 4 5


Output


2
3 1 4 2 5 

Note

In the example it's not possible to place ice spheres in any order so that Sage would buy 3 of them. If the ice spheres are placed like this (3, 1, 4, 2, 5), then Sage will buy two spheres: one for 1 and one for 2, because they are cheap.

Solution (in JAVA):

Solution:

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.Arrays;


public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		FastInput in = new FastInput(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		Cf671D solver = new Cf671D();
		solver.solve(1, in, out);
		out.close();
	}

	static class Cf671D {

		public void solve(int testNum, FastInput in, PrintWriter out) {

			int n = in.nextInt();
			int []prise = in.nextIntArray(n);
			Arrays.sort(prise);
			
			int []ans = new int [n];
			
			for(int i = 0 ; 2*i+1 < n ;i++) {
				ans[(i*2)+1] = prise[i];
			}
			for(int i = 0 ; 2*i < n ;i++) {
				ans[(i*2)] = prise[(n/2)+i];
			}
			
			int cnt = 0;
			
			for(int i = 1 ; i < n ; i+=2) {
				if(i == n-1) {
					break;
				}
				if(ans[i] < ans[i-1] && ans[i] < ans[i+1]) {
					cnt++;
				}
			}
			
			out.println(cnt);
			
			for(int i = 0 ; i < n ;i++) {
				if(i == n-1) {
					out.println(ans[i]);
				}
				else {
					out.print(ans[i]+" ");
				}
			}
		
			}


		}

	static class FastInput{
		private final BufferedReader in;
		private String[] buff;
		private int index = 0;
		
		public FastInput(InputStream is) {
			in = new BufferedReader(new InputStreamReader(is));
		}
		String nextLine() {
			try {
				return in.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return null;
		}
		String next() {
			while (buff == null || index >= buff.length) {
				buff = nextLine().split(" ");
				index = 0;
			}
			return buff[index++];
		}
		int nextInt() {
			return Integer.parseInt(next());
		}
		
		long nextLong() {
			return Long.parseLong(next());
		}
		
		Double nextDouble() {
			return Double.parseDouble(next());
		}
		
		BigInteger nextBigInteger() {
			return new BigInteger(next());
		}
		
		BigDecimal nextBigDecimal() {
			return new BigDecimal(next());
		}
		
		public int[] nextIntArray(final int n) {
			final int[] res = new int [n];
			
			for(int i = 0 ; i < n ;i++) {
				res[i] = nextInt();
			}
			return res;
		}
		
		public long[] nextLongArray(final int n) {
			final long[] res= new long [n];
			
			for(int i = 0 ; i < n ;i++) {
				res[i] = nextLong();
			}
			return res;
		}
		
		public double[] nextDoubleArray(final int n ) {
			final double[] res = new double [n];
			
			for(int i = 0 ; i < n ;i++) {
				res[i] = nextDouble();
			}
			return res;
		}
		
		
		public int[][] nextInt2DArray(final int n , final int m){
			int [][]res = new int [n][m];
			
			for(int i = 0 ; i < n ;i++) {
				for(int j = 0 ; j < m ;j++) {
					res[i][j] = nextInt();
				}
			}
			return res;
		}
		public long[][] nextLong2DArray(final int n , final int m){
			long [][]res = new long [n][m];
			
			for(int i = 0 ; i < n ;i++) {
				for(int j = 0 ; j < m ;j++) {
					res[i][j] = nextLong();
				}
			}
			return res;
		}
		
		public char[][] nextChar2DArray(final int n){
			char [][]res = new char [n][];
			
			for(int i = 0 ; i < n ;i++) {
				String s = next();
				res[i] = s.toCharArray();
			}
			
			return res;
		}
	}
}